How to make 3d Decals
Not sure if this is the result you're looking for, but if it is you can unwrap your object, projecting the UV-map from view (hotkey U). And then move and scale the UV-map over the normal texture (decal image.png).

Then when you apply the material to your object, it will look like this:

Edit:
(because comments do not allow for enough characters)
I thought you made a nice decal, and if you wanted it to be more 3D you could add it to your 3D model. I thought that was clear. Maybe a bit silly of me because i understand that often the point of using decals is to minimize the use of actual 3D geometry, So i did some digging.
It seems the Decal Machine Addon does not simply use normal maps. It adds to the illusion of geometry using parralax mapping or parralax occlusion. I don't know enough about it, but i believe that is currently not easy to do with Blender alone (hence, i suppose, the existence of the Decal Machine Addon)
Here are some resources on the subject (that also have .blend files implementing the technique):
https://devtalk.blender.org/t/parralax-occlusion-for-blender-2-8/3641 ,
https://blenderartists.org/t/parallax-shader-with-silhouette-clipping-for-blender-2-8-eevee-and-cycles/1162334
and
https://blenderartists.org/t/parallax-mapping-with-silhouette-clipping-shader-node/561285
They might be of more use to you than my answer